Estimating density from only unmarked individuals

[James Russell]

I have data in the form of spatially indexed detections of a small number of unmarked (unknown) individuals for a given level of effort. Assuming known values of g0 and sigma, I would like to estimate density or even abundance. Before I go about trying to solve this, I was wondering if anyone else has had a crack at a problem of this nature before?

 

A few caveats: I don't care about assigning detections to particular individuals, so long as I can estimate density (although a probabilistic assignment of records to particular individuals would not be turned down). In the first instance I am happy enough to assume mean (point) values of g0 and sigma, although ultimately a confidence interval for D which includes assumed variability in g0 and sigma would be preferred.

 

I would like to implement this in SECR as I generally like SECR and ultimately may end up with data combining a mix of marked and unmarked individuals from another project. At this time though, I am wanting to try and implement this as a special case of SECR mark-resight methods where the only data are sightings of a small number of unmarked individuals.

 

Using the help file code for mark-resight in SECR I’ve hit my first obstacle trying to implement this:

 

# Let’s take the MRCH example dataset but import no captures and note no marking occasions

# captures.txt = sess1 NONE 5 A1

MRCH2 <- read.capthist(file.choose(), file.choose(), detector = "proximity", markocc = c(0,0,0,0,0), verify = FALSE)

Warning message:

In read.table(file = "D:\\Research\\National\\ZIP\\mark-resight\\captures.txt",  :

  incomplete final line found by readTableHeader on 'D:\Research\National\ZIP\mark-resight\captures.txt'

# I will assume this warning message is not fatal

 

# Let’s add the Tu.txt example file

MRCH2 <- addSightings(MRCH2,unmarked=file.choose())

# a check with sightingPlot shows this is all OK

sightingPlot(MRCH2, "Tu", mean = FALSE, border = 20, fill = TRUE, col = "blue",

             legend = c(1,2,3), px = 1.0, py = c(0.85,0.72), xpd = TRUE)

 

# try fitting a model

fit1 <- secr.fit(MRCH2, model = list(g0=0.1,sigma=25,pID=1),verify=FALSE) # about same as for S in fit0

Error: $ operator is invalid for atomic vectors

In addition: Warning messages:

1: In secr.fit(MRCH2, model = list(g0 = 0.1, sigma = 25, pID = 1),  :

  using default buffer width 100 m

2: In secr.fit(MRCH2, model = list(g0 = 0.1, sigma = 25, pID = 1),  :

  0 detection histories

# I get a fatal error which I wonder if it has something to do with the nature of the data (i.e. no known captures).

 

Any help or suggestions for other methods to solve this problem appreciated.

 

James

[Murray Efford]

If you know g0 (lambda0), sigma and sampling effort then I suspect there is nothing more to be learned from the spatial distribution of detections and you can put aside mark-resight etc. Can you clarify the nature of your unmarked detections - are they n distinct individuals or merely un-individuated cues? If the former then D-hat = n/a(g0,sigma) works just fine, given that a(g0,sigma) takes account of the spatial distribution and intensity of sampling effort. If we're talking about a certain number of cues C, rather than n, then possibly D-hat = C/E(C|D=1) using the function Enrm in secrdesign 2.5.2 to compute E(C) (see secrdesign-tools.pdf).
Murray

[Murray Efford]

I meant to refer you to secrdesign-Enrm.pdf, but you could get there from secrdesign-tools.pdf